Downing Street yesterday dismissed calls for the education secretary, Ruth Kelly, to resign after a spate of fresh claims at the weekend about decisions by the education department clearing sex offenders to work in schools.

However, ministers are almost certain to be stripped of the responsibility for such decisions following the controversy, which shows no signs of dying out despite Ms Kelly's statement to the House of Commons last week.

The education secretary launched an "exhaustive review" of the vetting system for teachers cautioned and convicted of child sex offences after it emerged that a minister had cleared a PE instructor, Paul Reeve, to work in a Norfolk school despite receiving a police caution for viewing child pornography. He had not been placed on List 99, which bars such men from working in schools for life.

Officials at the Department for Education and Skills are understood to have worked through the weekend to attempt to determine how many such cases ministers have handled. But there was fresh controversy as it emerged that:

· Norfolk police and Norfolk county council wrote to the Home Office and the department in December about their concerns that Mr Reeve was not on list 99.

· Teachers on list 99 have in any case been cleared to work in specific schools: Keith Hudson, from Sussex, for example, was given permission to work in all-girl schools because medical evidence suggested his "paedophilic" impulses were directed only at boys.

· The Sunday Telegraph alleged that Ms Kelly had personally cleared a man convicted of indecently assaulting a 15-year-old to return to teaching, citing a letter from one of her officials last January. It told William Gibson that the education secretary had "given weight to the fact that you accept that your actions were unwise and your behaviour was unacceptable".

The shadow education secretary, David Willetts, said: "It is now a week since the original revelation of a sex offender being allowed to work in schools. Parents and teachers are now more confused than ever about the extraordinarily complicated regime that ministers have operated. The secretary of state has not answered the key questions and has not given a straightforward explanation of how the system works. That is why confidence in her is ebbing away."

The former Tory leader Michael Howard called in a newspaper article for her resignation, and Chris Woodhead, the former chief inspector of schools, told the BBC: "A secretary of state used to take responsibility ... They said no, the buck stops with me, I'm going to go. So she should."

Ian Gibson, the Labour backbencher whose Norwich North constituency covers the school where Mr Reeve was given a job, told BBC Radio 4 that the education secretary would need "good answers to some of the questions that are beginning to emerge" by the middle of the week.

One supportive senior Labour backbencher suggested she would be in trouble if more than 10 offenders had been cleared by the department on her watch, or if she had personally cleared a sex offender, because she had not said so already.

Downing Street yesterday insisted that Ms Kelly had the prime minister's full confidence, and the education department refused to give any more details about how many cases have been uncovered.

"We have announced a review into the decision making process in these cases and will report back shortly," it said. "We have been clear throughout that there is a responsibility on all employers, schools and supply agencies to carry out the necessary checks on permanent and supply teachers. List 99 exists alongside Criminal Review Board checks, not in isolation.

"Clearly, we are also looking at the criteria under which ministers are asked to make these decisions."

While education department officials insist that no decision has yet been taken on whether to remove ministerial responsibility, it is understood that is the favoured option.

But former ministers warned that the move could backfire, arguing that it would mean handing it to unaccountable officials or expecting the teaching profession to police itself.

The Liberal Democrat education spokesman, Ed Davey, said the change would be a positive step but would not tackle the real problem, which was that the information and checking systems for child protection were not working.

Margaret Morrissey, spokeswoman for the National Confederation of Parent Teacher Associations, said more than 100 parents had contacted her with concerns about convicted sex offenders working in schools. "There is a feeling [amongst parents] that if the secretary of state had such little grasp as to what was happening in one of the most important areas of her department it needs to be looked at," she said.

What critics say

Ruth Kelly faces three key criticisms

·She is taking too long to come clean over the full scale of the issue. DfES officials worked over the weekend to try to determine how many cases exist, but do not want to make any announcement until they are certain. It is thought some information is not computerised and may only exist in paper form.

·She has not acted on the recommendations of the Bichard inquiry, which followed the Soham murders. She announced last week that the necessary legislation will come before the house next month, but will not come into effect until 2008.

·She is not on top of her brief. The education department is bigger than ever, having acquired responsibility for all aspects of child policy shortly before she took over. She is also attempting to steer through the government's controversial white paper on schools.